Final%20Exam%20Lectures%20EM%20Waves%20and%20Optics - PowerPoint PPT Presentation

View by Category
About This Presentation
Title:

Final%20Exam%20Lectures%20EM%20Waves%20and%20Optics

Description:

Final Exam Lectures EM Waves and Optics – PowerPoint PPT presentation

Number of Views:56
Avg rating:3.0/5.0
Slides: 82
Provided by: Beatr67
Learn more at: http://web.nmsu.edu
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Final%20Exam%20Lectures%20EM%20Waves%20and%20Optics


1
Final Exam Lectures EM Waves and Optics
2
Electromagnetic Spectrum
3
Traveling EM Wave
  • Maxwells equations predict the existence of em
    waves propagating through space at the speed of
    light
  • The waves consist of oscillating E and B fields
    that are perpendicular to each other and the
    direction of wave propagation

4
EM Waves cont
  • EM waves generated with transformers and LC
    circuits
  • EM waves is composed of changing E and B fields
    and will therefore travel in a vacuum
  • Maxwells equations can be used to develop a wave
    equation from which the form of the waves can be
    deduced

5
Properties of EM Waves
  • The solutions of Maxwells equations are
    wavelike, with both B and E satisfying a wave
    equation.
  • EM waves travel through a vacuum at the speed of
    light.
  • The components of the E and B fields of plane em
    waves are perpendicular to each other and to the
    direction of propagation (transverse waves)
  • The magnitudes of E and B in empty space are
    related by the expression
  • EM waves obey the principle of superposition

6
Energy Transport
  • Poynting vectorthe rate of energy transport per
    unit area in an em wave
  • Its units are
  • The direction of the Poynting vector is the
    direction of wave propagation
  • Intensitythe time averaged value of S over one
    or more cycles

7
Radiation Pressure
  • Radiation pressure is the linear momentum
    transported by an em wave
  • If the surface absorbs all the incident energy
  • An example of this type of surface is a black
    body
  • If the surface is perfectly reflecting for a
    normally incident wave
  • An example of this type of surface is a mirror

8
Optics Definitions
  • Geometrical opticsthe study of the properties of
    light waves under the approximation that it
    travels as a straight line (plane wave)
  • Reflectionwhen light hits a surface and bounces
    back
  • Refractiontravel of light through a surface (or
    interface) that separates 2 media. Light is bent
    at the surface, but inside the medium it travels
    in a straight line

9
  • Index of refraction nassociated with a medium of
    travel. It also depends on the wavelength of
    light for all media except vacuum.
  • Angle of incidence ?Ithe angle the light makes
    to the normal to the surface when it hits the
    surface
  • Angle of reflection ?r the angle the light makes
    to the normal to the surface when it bounces back
  • Angle of transmission ?t the angle the light
    makes to the normal to the surface inside the
    surface

10
Polarization
  • Polarization em waves which vibrate randomly in
    all directions are made to vibrate in one
    direction
  • An E field component parallel to the polarizing
    direction is passed (transmitted) by a polarizing
    sheet a component perpendicular to it is absorbed

11
Reflection
  • Law of reflection the angle of incidence equals
    the angle of reflection
  • Total internal reflection when all light
    incident on a surface is reflected

12
Refraction
  • Refraction the travel of light through an
    interface (bending of light by an interface)
  • Law of refraction (Snell's Law)

13
Definitions
  • Imagethe reproduction derived from light of an
    object. Images are located either at a point
    from which light rays actually diverge or at the
    point from which they appear to diverge.
  • Virtual imageimage perceived to be on the
    opposite side of the mirror from the object and
    observer (no actual light)
  • Real imageimage perceived to be on the same side
    of the mirror as the object and observer (light)

14
More Definitions
  • Mirrora surface which reflects a beam of light
    in one direction, not scattering or absorbing it
  • Plane mirrora flat reflecting surface (mirror).
    Light diverges after reflection from this type of
    mirror.
  • Spherical mirrora mirror with a reflecting
    surface like a section of a sphere. This mirror
    focuses incoming parallel waves to a point

15
More Definitions
  • Image length (i ) the perpendicular distance of
    an image from the center of the mirror
  • Object length (p)the perpendicular distance of
    the object from the center of the mirror
  • Magnification (M)a measure of the size of the
    image compared to the size of the object

16
Facts About all Mirrors
  • the angle of incidence equals the angle of
    reflection
  • p is positive for all images. Using the
    convention an object or image in front of the
    mirror (or the side light or an observer is) is
    positive and an object or image behind the mirror
    would be negative.
  • i is negative for virtual images, and positive
    for real images

17
Plane Mirrors
  • The magnification is always 1.
  • The image is as far behind the mirror as the
    object is in front of it (p -i).
  • The image is virtual and upright (same
    orientation as the object).
  • The image has front-back reversal

18
Finding Images
  • Point Source
  • Draw 2 rays extending from the object to the
    mirror
  • Using law of reflection, reflect the 2 rays off
    the mirror
  • Extend the reflections back till the point where
    they join
  • This is the image of the point
  • Extended Source
  • Do the above steps for a point at the top of the
    object and for a point at the bottom of the
    object
  • Draw in the rest

19
Spherical Mirror Definitions
  • Concavecaved in spheres, looking from the
    interior of the sphere. Light rays converge to a
    real point after reflection therefore there is a
    real focus
  • Convexflexed out spheres, looking from the
    exterior of the sphere. Light rays diverge after
    reflection therefore there is a virtual focus

20
More Spherical Mirror Definitions
  • Central (principal) axisextends through the
    center of curvature of the sphere and through the
    center of the mirror
  • Paraxial raysrays which diverge from the object
    to make a small angle with the principal axis
  • Focus (focal point)point through which all
    paraxial rays parallel to central axis reflect
    through (a point on the central axis), or their
    extensions for a convex mirror
  • Focal length (f)the distance of the focus from
    the center of the mirror

21
Concave Mirror Facts
  • There is a smaller field of view than with plane
    mirrors.
  • The image is greater in size than the object.
  • The focus is real.
  • As the object is moved closer to the focal point,
    the real, inverted image moves to the left. When
    the object is on the focal point the image is
    infinitely far to the left. When the object
    moves past the focal point toward the mirror, the
    image is virtual, upright, and enlarged.
  • For a concave mirror the image goes out to
    infinity for pltf (m increases) and image comes in
    from infinity for pgtf (m increases from -infinity
    to 0)

22
Convex Mirror Facts
  • There is a greater field of view than with plane
    mirrors.
  • The image is smaller in size than the object.
  • The focus is virtual.
  • As the object distance increases, the virtual
    image decreases in size and approaches the focal
    point as the object distance approaches infinity

23
Locating Images By Drawing Rays
  • A ray parallel to the central axis reflects
    through the focal point.
  • A ray passing through the focal point reflects
    parallel to the central axis.
  • A ray passing through the center of curvature
    reflects along itself.
  • A ray reflecting at the center of the mirror is
    reflected symmetrically about the central axis

24
(No Transcript)
25
Mirror Type Plane Concave Concave Convex
i -p p lt f p gt f i lt p
Magnification M 1 M gt 1 M lt 0 0 lt M lt 1
Image Virtual Virtual Real Virtual
Orientation Same Same Inverted Same
Sign of f No f -
26
Lens Definitions
  • Lensa transparent object with two refracting
    surfaces whose central axes coincide (image
    formed by first serves as the object for the
    second)
  • Converging lenscauses a light ray that is
    initially parallel to the central axis to
    converge to a point
  • Diverging lenscauses a light ray that is
    initially parallel to diverge
  • Thin lensthickness of lens is much less than p,
    i, r1, r2 (r1 is the radius of curvature of the
    first lens surface and r2 is the radius of
    curvature of the other lens surface)

27
Refraction
  • If
  • Then
  • If
  • Then
  • Bend toward normal
  • If
  • Then
  • Bend away from normal

28
Refraction from Spherical Surfaces
  • If rays are bent toward the central axis, they
    form a real image on that axis on the opposite
    side of the surface from the object ( i)
  • If rays are bent away from the central axis, they
    form a virtual image on that axis on the same
    side of the surface from the object (- i)

29
Spherical Surface Planar Surface
30
(No Transcript)
31
Refraction cont
  • convex surface is a converging lens
  • concave surface is a diverging lens

32
Images from Thin Lenses
  • A ray initially parallel to the central axis will
    pass through the focal point f.
  • A ray initially passing through the focal point f
    (or its backward extension) emerges parallel to
    the central axis.
  • A ray initially directed toward the center of the
    lens will emerge with no direction change

33
(No Transcript)
34
Lens Type Converging (Convex) Diverging (Concave)
p gt f1 p lt f1
Magnification M lt 0 M gt 1 0 lt M lt 1
Image Real Virtual Virtual
Orientation Inverted Same Same
Sign of f -
35
Object produces image in 1st lens which is the
object for the 2nd.
36
Two Lens Systems
  • Find the image formed by the first lens as if the
    second lens is not present
  • Draw a ray diagram for the second lens with the
    image of lens 1 as the object of lens 2
  • The second image formed is the final image for
    the system
  • One configuration of this is if the image formed
    by the first lens is behind the second lens and
    is used as a virtual object for the second lens
  • The total magnification of the system will be

37
Human Eye
38
Human Eye
  • Light enters the eye through the cornea, a
    transparent structure.
  • Behind the cornea is a clear liquid called the
    aqueous humor.
  • Next is a variable aperture called the pupil,
    which is an opening in the iris.

39
Human Eye cont
  • Next is a crystalline lens. The purpose of the
    crystalline lens is to allow the eye to focus on
    an object through a process called accommodation.
    The ciliary muscle is situated in a circle
    around the lens. Thin filaments called zonules
    run from the muscle to the lens
  • To focus the eye on a far object, the ciliary
    muscle is relaxed which tightens the zonules on
    the lens forcing it to flatten and increase its
    focal length
  • To focus the eye on a near object, the ciliary
    muscle is tightened which relaxes the zonules on
    the lens allowing it to bulge and decrease its
    focal length

40
Human Eye cont
  • Most refraction occurs at the outer surface of
    the eye, where the cornea is covered with a film
    of tears. Very little occurs in the lens because
    the aqueous humor and the lens have very similar
    index of refractions
  • The iris is a muscular diaphragm that controls
    the pupil size and therefore the intensity of
    light that gets into the eye
  • The cornea lens system of the eye focuses light
    onto the back surface of the eye called the
    retina, consisting of millions of little
    receptors called rods and cones. When these
    receptors are stimulated by light they send a
    signal to the brain by way of the optic nerve
  • In the brain the image is perceived and analyzed

41
Nearsightedness
  • In nearsightedness the rays converge before they
    meet the retina. A nearsighted person sees close
    objects but not far. This means the far point is
    much closer than infinity. A diverging lens
    before the eye corrects this condition

42
Farsightedness
  • In farsightedness the light rays reach the retina
    before they converge. A farsighted person can
    see far away objects but not near objects. That
    means their near point is much farther away than
    25 cm. The condition is corrected by putting a
    converging lens before the eye

43
Two Lens Systems
  • Find the image formed by the first lens as if the
    second lens is not present
  • Draw a ray diagram for the second lens with the
    image of lens 1 as the object of lens 2
  • The second image formed is the final image for
    the system
  • One configuration of this is if the image formed
    by the first lens is behind the second lens and
    is used as a virtual object for the second lens
  • The total magnification of the system will be

44
Microscope
  • Microscope used to view small objects with a
    combination of two lenses to get greater
    magnification
  • One lens is called the objective and has a very
    short focal length (lt 1 cm)
  • The second lens is called the eyepiece and has a
    longer focal length of a few centimeters

45
Telescope
  • Two types of telescopes are used to view distant
    objects, such as the planets in our Solar System
  • The refracting telescope uses a combination of
    lenses to form an image (uses two lenses, the
    objective and the eyepiece)
  • The reflecting telescope uses a curved mirror and
    a lens

46
Aberrations
  • Two types
  • Spherical aberrations occur because the focal
    points of rays far from the principal axis of a
    spherical lens are different from the focal
    points of rays of the same wavelength passing
    near the axis (paraxial rays) Minimized by
    adjustable apertures or parabolic reflecting
    surfaces
  • Chromatic aberrations occur because different
    wavelengths of light refracted from a lens focus
    at different points Minimized by use of a
    combination of a converging lens made of one type
    of glass and a diverging lens made of another
    type of glass

47
Interference
  • Interference phenomena occur when 2 waves
    combine.
  • The effects occur where light reflected from the
    front and back surfaces of a film interfere with
    each other.
  • Examples are colors seen in oil films or soap
    bubbles.

48
(No Transcript)
49
(No Transcript)
50
(No Transcript)
51
Diffraction
  • Diffraction occurs when many sources are present.
  • These effect occur whenever a wave passes through
    an aperture or around an obstacle.

52
Relativity Lecture
  • Relativity
  • Time Dilation
  • Length Contraction
  • Transformation Equations
  • Review

53
Postulates
  • Relativity postulate the laws of physics are
    the same for observers in all inertial reference
    frames
  • Einstein extended this from Galileo (laws of
    mechanics) to include electromagnetism and optics
  • Speed of light postulate the speed of light in
    vacuum has the same value c in all directions and
    in all inertial reference frames
  • Ultimate speed-no entity which carries energy or
    information can exceed this limit c299792458
  • Inertial reference frame frames in which
    Newtons laws are valid (nonaccelerating)

54
Events
  • Event something that happens to which an
    observer can assign a set of coordinates
  • Space, time, or spacetime

Construction to help picture spacetime X
coordinate from measuring rods and time
coordinate from clocks
55
Relativity
  • Relativity deals with the measurement of events
    and how they are related
  • If two observers are in relative motion, they
    will not, in general, agree as to whether two
    events are simultaneous

56
Relativity - Simultaneity
  • Consider Sam and Sally to the left
  • Blue and Red events occur
  • Sam sees them as simultaneous
  • Sally sees the red event first (before Sam does),
    and the blue event later
  • Note both measure themselves halfway in between
    (Sam conclude simultaneous and Sally concludes
    red event happens first)

57
Time Dilation
  • The time interval between two events depends on
    how far apart they occur, in both space and time
  • Proper time interval the time interval between
    two events, which occur at the same location in
    an inertial reference frame, measured in that
    frame
  • Measurements of the same time interval in any
    other inertial reference frame are always greater

58
Time Dilation cont
59
Length Contraction
  • The length of an object depends on which
    reference frame it is measured in
  • Proper length (rest length) the length of an
    object measured in the rest frame of the object
  • Measurements of the same length in any other
    inertial reference frame are always less
  • Length contraction occurs only along the
    direction of relative motion

60
Transformation Equations
Lorentz Transformation Equations
Galilean Transformation Equations
61
Velocities
  • Using the Lorentz eqs. we can compare the
    velocities observed by 2 observers in frames
    moving relative to each other

62
Momentum
  • Momentum is also effected by speed
  • Classically pmv
  • Relativistically

63
Mass Energy
  • Mass and energy are conserved together not
    separately as assumed classically
  • Nuclear reactions show us this
  • Rest energy or mass energy
  • Use units

64
Energy cont
It is impossible to increase speed to c because
it would require an infinite amount of energy
  • The total energy (without potential energy)

65
Review
  • Ch 22 26 deals with electrostatics (charges
    that are not moving)
  • Ch 26 28 deals with electrodynamics (moving
    charges)
  • Ch 29 31 are dealing with magnetism an effect
    of moving charges
  • Ch 32 33 deals with combining electricity and
    magnetism plus some of the uses of these concepts
  • Ch 34 37 deals with geometric optics
  • Ch 38 deals with relativity

66
Radiation Lecture
  • Nuclear Physics
  • Nuclear Properties
  • Radioactive Decay
  • Radioactive Dating
  • Radiation Dosage

67
Nuclear Physics History
  • Nuclear Physics the study of the nucleus of the
    atom
  • Plum pudding model the original theory of atom
    structure, postulated by JJ Thompson. The
    positive charge of the atom is spread throughout
    the entire atom volume. The electrons vibrated
    at fixed points within the sphere of positive
    charge.
  • Nuclear model positive charge of atom is
    densely concentrated at the center of the atom
    (nucleus), postulated by Ernest Rutherford.

68
Experiment for Nuclear model
  • An alpha particle source (radon gas) shot alpha
    particles at a gold foil.
  • The angle of deflection of these particles was
    studied.
  • Most particles were deflected through small
    angles
  • A few were deflected through large angles
    approaching 180 degrees.
  • Analysis of the data implied the radius of the
    nucleus was 104 times smaller than the radius of
    the atom

69
Nuclear Properties
  • Nucleus made up of protons and neutrons
  • Atomic number Z - of protons
  • Neutron number N - of neutrons
  • Mass number A - of both protons neutrons

or
Gold for example
70
Isotopes
  • Isotopes nuclide with same Z but different A
    (different of neutrons)
  • For a given element, they have the same
    electrons and therefore the same chemical
    properties
  • The nuclear properties vary from 1 isotope to
    another.
  • Usually an element has one stable isotope and the
    rest are radioactive and decay by emitting a
    particle.

71
Nuclidic Chart
  • There is a well defined band of stable nuclides
    (green) with unstable above, below, and the upper
    end of the chart.
  • Light stable NZ
  • Heavy stable NgtZ

72
Binding Energy
  • Binding energy difference between mass M of a
    nucleus and the sum of the masses of its
    individual protons and neutrons
  • Binding energy is a convenient measure of how
    well a nucleus is held together

73
(No Transcript)
74
  • The nuclei high on the plot are very tightly
    bound. (Ni)
  • Those low on the plot are less tightly bound. (H
    U)
  • Consequence
  • Right side nuclei would be more tightly bound if
    split into 2 nuclei farther up the plot in the
    process fission.
  • Left side nuclei would be more tightly bound if
    combined to form nucleus closer to top in the
    process fusion

75
Radioactive Decay
  • Radioactive decay follows statistical laws.
  • A 1 mg sample of U has ?1018 atoms. During any
    second only 12 of them will decay and it is
    impossible to predict which 12 will do it. All
    have the same chance.
  • Decay rate
  • is decay constant (value is characteristic of
    every radio nuclide
  • N is in the sample at a given time
  • R is the decay rate at a given time

76
Activity of a Sample
  • R is called the activity of a sample
  • 1 bacquerel 1 Bq 1 decay/s
  • 1 curie 1 Ci 3.7x1010 Bq
  • Half life ( ) the amount of time in which
    both N R are reduced to half their original
    value
  • Mean life (?) the amount of time in which both
    N R are reduced to e of their original value

77
Decay
  • Alpha Decay nucleus emits an alpha particle
  • Beta Decay nucleus emits an electron or
    positron
  • Gamma Decay nucleus emits a photon or gamma ray

78
Alpha Decay
  • The nucleus emits an alpha particle and
    transforms to a different nuclide.
  • Spontaneous because total mass of the decay
    products is less than the mass of the original
  • Disintegration energy (Q) the difference
    between the initial mass energy and the total
    final mass energy

79
Beta Decay
  • The nucleus emits an electron or positron
  • ? is a neutrino

80
Radiation Dosage
  • Absorbed Dose a measure of the radiation dose
    actually absorbed by a specific object
  • SI unit 1 gray 1Gy 1 J/kg
  • Dose Equivalent the biological effect of a
    radiation source (found by multiplying absorbed
    dose by RBE)
  • SI unit 1 sievert 1 Sv 100 rem
  • RBE (Relative Biological Factor)
  • Radiation RBE
  • Electron x rays 1
  • Slow neutrons 5
  • Alpha particles 10

81
  • A whole body short term gamma ray dose of 3 Gy
    will cause death in 50 of the population exposed
    to it.
  • Recommended radiation exposure is lt
    5mSv in a year.
About PowerShow.com